Self-excitation of mutually phase-conjugated light waves in a cubic gyrotropic photorefractive crystal subjected to a square-wave electric field

Stationary four-wave mixing in a shifted photorefractive transmission grating formed in cubic gyrotropic crystals of the 23 symmetry is considered in the case of low contrasts of the original optical interference pattern. Expressions for the transmission and reflection coefficients for the phase conjugation of weak light beams in arbitrarily cut samples are obtained by solving exactly the equations for the coupled waves that include the effects of the natural circular birefringence and the linear birefringence induced by the external field. The conditions for the generation of phase-conjugated waves are determined for the mixing at 633 nm in Bi$_{12}$SiO$_{20}$ and Bi$_{12}$TiO$_{20}$ samples in the case when the grating vector is parallel to the [$\bar{1}10$] axis and the incident pump waves propagate in the (001) crystal plane and have arbitrary polarisations.